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J.Phys.D.App\.Phys.28(1995)1537-1546.PrintedintheUKIITheoryofthemagnetomechanicaleffectDCJilesAmesLaboratory,IowaStateUniversity,Ames,IA50011,USAReceived31January1995,infinalform10April1995Abstract.ThisstLdyinvestigatedamodeltheoryofthechangesinmagnetizationthatalerromagneticmaterialundergoeswhensubjectedtoanappliedmiaxialstress.Thedescriptionoftheseeffectsisshowntooetotallydifferentfromthedescr:pt.onofthecnangesinthehysteresisctunderaseries01constantappliedstresses.Themainmechanismintheproposedmodeltheoryistheunpinning01clomainwallsbytheapplicationofstress,whichallowsthewallstomoveandcausesachangeinthemagnetization.Thiscnangeinmagnetizationreducestnedisplacementfromtheanhystereticmagnettzation.Inaddition,theanhystereticmagnetizationitselfischangedbytneapplicationofstressviathemagnetoelasticcoupl'ng.Itisshownthattheeffectcanbedescrioedbyanequationin*hichtherateofchangeofmagnetizationwithelasticenergyisproporlionatto!hedisplacementofthemagnet.zalionfromtheanhystereticmagnetization.Thisistermedthe'law01approach'.Thislawseemstoapplywhenthestartingconditionofthematerialisonamajorhysteresisloop.1.IntroductionInrecentyearstherehasbeenaresurgenceofinterestinanoldproblemthatwasneveradequatelyexplained.Themagnetomechanicaleffect,thatisthechangeofmagnetizationofamagneticmaterialresultingfromtheapplicationofstress,hasattractedattentionbecauseofitsrelevancetoseveraltechnologicalproblems,includingthetendencyofpreviousunmagnetizedlargestructurestobecomemagnetizedwhenstressedinthepresenceoftheearth'smagneticfield,theuseofmagneticmaterialsinsensors,thetendencyofmagnetizedmaterialstohavetheirmagnetizationreducedafterstressingandapplicationsofmagneticmethodstothenon-destrxtiveevaluationofstressinmaterials.Inthispaperaphenomenologicaltheoryisdeveloped,whichcanexplainpreviousobservationsandhasbeenusedtodevelopapredictivecomputermodelfordetermininghowamaterialbehavesunderawiderangeofconditionsofmagneticfieldandstress.Theoriginalapproachtotheproblemofthemagnetomechanicaleffectwastoassumethattheprocessisreversible.Inthisapproachitwasarguedthat,sinceamagneticmaterialchangesitslengthwhenitismagnetized,itisreasonabletoexpectthatitsmagnetizationwillchangewhenitisstrained.ThisideawasdiscussedbyBozorth[I].Cullity[2]evendiscussedtheseeffectsintermsofLeChatelier'sprinciple.Forsmallreversiblechangesathermodynamicrelationdoesexist,namely=(E)where(dh/dH),istherateofchangeofmagnetostric-tionwithmagneticfieldatconstantstressand(dB/du),0022-3727/95/081537+10%19.50@1995IOPPublishingLMisthechangeofmagneticinductionwithstressatcon-stantfield.(IntheSIsystem,theunitsofBarekgA-'s-'andtheunitsofUarekgm-'s-*,sothat(dB/do)hasunitsofmA-'.)SinceB=po(H+M),andHisnotafunctionofstress,thislatterexpres-sionisequaltopo(dM/dc)H,whichisthederivativeofinterestinthemagnetomechanicaleffect.Equation(1)merelyshowsthat,forreversibleprocesses,alargemag-netomechanicaleffect(dB/do)shouldbeobservedinmaterialswithalargemagnetostrictivestrainderivativeInfact,theaboveequationisquitemisleadingasadescriptionofthemagnetomechanicaleffectinferromagneticmaterialsbecausethemagnetizationprocessishystereticandthereforeinherentlyirreversibleinnature,althoughreversiblechangesinmagnetizationaresuperposedontheirreversiblechanges.Therefore,adescriptionoftheprocessmustbeintimatelyconnectedwithadescriptionofirreversibilityandhysteresis.Previousworkonthedevelopmentofmodeltheoriesofthemagnetizationprocessesinferromagneticmaterialshaveconcentratedonthedescriptionofhysteresis[3,4]andthechangesinhysteresiscurvesthatresultfromconstantappliedstress[5].Themagnetomechanicaleffect,whichisdefinedasthechangeinmagnetizationofamagneticmaterialresultingfromachangeinappliedstressunderaconstantappliedfield,hasbeenreportedoccasionally[6,7],buttheeffectshaveappearedtobeverycomplex.Forexample,inthecloselyrelatedworksofCraikandWood[8]andofBirss,FaunceandIsaac[9],theexperimentalresultswereobtainedbyapplyingstressestovariouspolycrystallinemagneticmaterialsinthepresenceofasmallconstantmagneticfield.Itwasnoted1537(dh/dH)c.DCJilesthatthereweremanyfeaturesintheresultsthatcouldnotbereconciledwiththeprevioustheoryofBrown[IO].Inparticularitwasnoticedthatverycleardifferencesbetweentheeffectscausedbytensionandcompressionwerenotinterpretableintermsoftheexistingtheory.InBrown'stheoryitwasassumedthatthechangeinmagnetizationduetodomainwallmotionobeyedRayleigh'slaw[I11atlowmagnetizations.Fromthisatheoreticalcurveofmagnetizationversusstresswasderived,basedontheideathatbothmagneticfieldandstressarethermodynamicallyequivalenttoapressureonthemagneticdomainwalls.Inthisapproach,stresswastreatedasequivalenttoamagneticfield,whereasinfacttheeffectofstressisactuallyequivalenttotheimpositionofanadditionalanisotropyenergy.Thisapproachhassomefundamentalproblems.Stressisatensorandmagneticfieldisavector,andthereforetheyhavedifferentsymmetries.However,evenifthislimitationisoverlooked,asignificantproblemofthetheorydevelopedbyBrownwasthatexactlythesamechangesinmagnetizationwerepredictedunderbothtensionandcompression.Thiswasexplainedbyconsiderin